Verdicts and judgments on her period in office are going to be flooding in over the next few days.

It's certainly the case that she was set an impossible problem with delivering Brexit.

But she made that problem immeasurably harder for herself by her failure to communicate her own strategy for doing so.

"Brexit means Brexit, and we're going to make a success of it."

She started off as an imperious figure going out to bat for Britain, and get a great deal, and show strength rather than weakness.

She ended up arguing for compromise.

And If you're going to do that you have to start off arguing for compromise, not get there at the end.

"In order to get the best deal for Britain we need to ensure we've got that strong and stable leadership."

In the end she's been let down by her shortcomings as a political tactician and a political operator, as much as by the complexity of the situation that she faced.

Her game plan was to deliver Brexit, to get a deal with the European Union, and to keep the Conservative party together at the same time.

And these three things were very, very hard to reconcile.

So what comes next?

Well there's going to be a Conservative party leadership election.

It's going to start the week of June the 10th.

It'll be whittled down to a shortlist of two by MPs over the course of that week, and then Conservative party members will choose the successor.

"Do you think you're too divisive a character to be Tory leader?"

The front-runner to succeed her will certainly be Boris Johnson, the former foreign secretary and leading figure in the Leave campaign.

But the Conservative party has a track record of not picking its front-runners, and this is going to be a very, very large field.

So you certainly can't take it for granted that he's going to emerge as the winner in the end.

So where does this actually leave the issue of Brexit, the issue that has fundamentally brought down Theresa May?

The obvious immediate conclusion is that it makes a no-deal exit more likely, but that's not the same as making it definite.

None of the candidates are actually going to advocate a no-deal Brexit.

But what they will say is that they are prepared to see a no-deal Brexit if they can't get the right deal for Britain.

And in particular, that means junking the hated Northern Ireland backstop designed to create a frictionless border between Northern Ireland and the Republic of Ireland.

The fundamental problem with going down that path remains the hostility of the House of Commons, which does not want to see a no-deal Brexit.

It is true that constitutionally it's very hard to stop a prime minister set on doing this.

But there are ways, including a vote of confidence designed to bring down the government.

That would require some Conservatives being ready to bring down their party in order to prevent this.

But there are a handful who might be prepared to do that.

And the Conservatives will know that a general election at this time is not a welcome prospect.

They will all be very scared of it.

And none of them will want to elect a leader who's going to plunge them into a general election very soon.

Especially after what we expect to be catastrophic European parliamentary elections.

We get the results Sunday night and Monday morning.

They're almost certain to be the worst results the Conservative party have ever had in any election ever.

"It will be for my successor to seek a way forward that honours the result of the referendum."

"To succeed, he or she will have to find consensus in parliament, where I have not."

"Such a consensus can only be reached if those on all sides of the debate are willing to compromise."

The most interesting part of Theresa May's resignation speech in Downing Street was where she said:

That the next leader is going to have to proceed in the spirit of compromise.

They're going to have to find a compromise.

And that was very interesting because the party clearly is in no mood to compromise over Brexit.

The leader may have changed but the parliamentary arithmetic and the problems have not.